If you open the first few pages of O'Reilly's Beautiful Code, you will find a well written chapter by Brian Kernighan (Personal motto: "No, I didn't invent C. Who told you that?"). The non-C inventing professor describes how a limited form of regular expressions can be implemented elegantly in only a few lines of C code.

Let's say you have millions of pictures of faces tagged with names. Given a new photo, how do you find the name of person that the photo most resembles?

In the cases I mentioned, each record has hundreds or thousands of elements: the pixels in a photo, or patterns in a sound snippet, or web usage data. These records can be regarded as points in high dimensional space. When you look at a points in space, they tend to form clusters, and you can infer a lot by looking at ones nearby.